Question

The channel transition matrix of a binary channel is given by



If $P\left(x_0\right)=\frac{1}{3}$ and $P\left(x_1\right)=\frac{2}{3}$, then the ratio $\frac{P\left(y_1\right)}{P\left(y_o\right)}$ will be _______ .

• A. 2.46

Answer 1

The correct option is A 2.46
$\left[P\right(y_0\left)P\right(y_1\left)\right]=\left[P\right(x_0\left)P\right(x_1\left)\right]P\left[\frac{Y}{X}\right]=\left[\frac{1}{3}\frac{2}{3}\right]\left[\begin{array}{cc}\frac{2}{3}& \frac{1}{3}\\ \frac{1}{10}& \frac{9}{10}\end{array}\right]$
$=[\frac{2}{9}+\frac{2}{30}\frac{1}{9}+\frac{18}{30}]=\left[\frac{26}{90}\frac{64}{90}\right]$
$\frac{P\left(y_1\right)}{P\left(y_0\right)}=\frac{64}{26}=2.46$